I was hoping someone could provide some guidance on whether there is a
test in Stata for determining whether there is statistically significant
difference in ratios. In my case, I am examining committee seats and the
ratio of majority members to minority members and comparing that to the
chamber as a whole. Any thoughts?

Usually, when comparing 2 ratios, we measure ratios between ratios, not
differences between ratios. In your case, you seem to be looking for
logistic regression, which in Stata is handled by the -logit- procedure.
The odds in favour of being a minority member is defined as the probability
of being a minority member divided by the probability of being a majority
member. Logistic regression is used to derive confidence intervals for odds
and their ratios. In your case, you might have a binary variable
-minority-, which is 1 for minority members and 0 for majority members, and
a variable -committee-, which is 1 for committee members and 0 for
non-committee legislators. If you type

logit minority committee, or

then Stata will give you a confidence interval for the ratio between the
odds of being minority for committee members and the odds of being minority
for non-committee legislators. And if you typed

gene byte baseline=1
logit minority committee baseline, or noconst

then Stata will give you confidence intervals for the baseline odds of
being a minority (assuming that you are a non-committee legislator) and
also for the odds ratio as before.